Currently each of you has a share of 50% in the property , however if you wanted to sell or will your share away you can under the principal of tenant in common or co ownership. Since you are married the family home protection act steps in and this impacts you in that neither party can go off and sell their share. It seems that you are now looking for a joint tenancy agreement which states that on death the property automatically reverts to the remaining spouse or next of kin which ever is first.
Have a chat with your solicitor , it will be inexpensive and straight forward to do, but get it done as so many people in the republic tend to leave these things on the burner.
[broken link removed]